The curve C C\,C has parametric equations
x=2tx = 2tx=2t, y=t2−ky = t^2 - ky=t2−k
where k k\,k is a positive constant.
C C\,C meets the line y=xy = xy=x at two points, A A\,A and BBB.
Show that the xxx-coordinates of A A\,A and B B\,B satisfy
x2−4x−4k=0x^2 - 4x - 4k = 0x2−4x−4k=0
Given that the length of AB AB\,AB is 50\sqrt{50}50, find the value of kkk.
76 exam-style questions on WJEC A Level Maths 3.3 Coordinate geometry in the (x, y) plane (A-level only), covering 3.3.1 Coordinate geometry in the (x, y) plane (A-level only) and 3.3.2 Coordinate geometry in the (x, y) plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.